OTHER WAYS TO CONVEY THAT MEANING
같이 (으)세요: "Please do something with me" - more polite than (으)ㅂ시다; when suggesting or inviting a group of people of a higher status or who are older than you to do something (ex. 선생님이나 교수님)
(으)ㄹ까요: "Shall we" - used when the speaker wants to either suggest doing something together with the listener or ask about the listener's preference or opinion regarding doing something; also has another, different use (so study)
기로 해요: "Let's (decide to) do something" - refers to the speaker and listener making the promise, resolution, or decision to do something (together)
(Part 3)